Contact time on curved superhydrophobic surfaces

Jeonghoon Han, Wonjung Kim, Changwoo Bae, Dongwook Lee, Seungwon Shin, Youngsuk Nam, and Choongyeop Lee

Phys. Rev. E 101, 043108 – Published 24 April 2020

Abstract

When a water drop impinges on a flat superhydrophobic surface, it bounces off the surface after a certain dwelling time, which is determined by the Rayleigh inertial-capillary timescale. Recent works have demonstrated that this dwelling time (i.e., contact time) is modified on curved superhydrophobic surfaces, as the drop asymmetrically spreads over the surface. However, the contact time on the curved surfaces still remains poorly understood, while no successful physical model for the contact time has been proposed. Here, we propose that the asymmetric spreading on the curved surface is driven by either the Coanda effect or inertia depending on the ratio of the drop diameter to the curvature diameter. Then, based on scaling analysis, we develop the contact time model that successfully predicts the contact time measured under a wide range of experiment conditions such as different impact velocities and curvature diameters. We believe that our results illuminate the underlying mechanism for the asymmetric spreading over the curved surface, while the proposed contact time model can be utilized for the design of superhydrophobic surfaces for various thermal applications, where the thermal exchange between the surface and the water drop occurs via a direct physical contact.

Received 25 September 2019
Revised 19 March 2020
Accepted 25 March 2020

DOI:https://doi.org/10.1103/PhysRevE.101.043108

Physics Subject Headings (PhySH)

Drop & bubble phenomena Drop interactions Wetting

Fluid Dynamics

Authors & Affiliations

Jeonghoon Han ¹, Wonjung Kim ², Changwoo Bae ¹, Dongwook Lee³, Seungwon Shin³, Youngsuk Nam ^1,*, and Choongyeop Lee ^1,†

¹Department of Mechanical Engineering, Kyung Hee University, Yongin 17104, Republic of Korea
²Department of Mechanical Engineering, Sogang University, Seoul 04107, Republic of Korea
³Department of Mechanical and System Design Engineering, Hongik University, Seoul 04066, Republic of Korea

^*ysnam1@khu.ac.kr
^†cylee@khu.ac.kr

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Issue

Vol. 101, Iss. 4 — April 2020

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Images

Figure 1
(a) Schematic of drop impact experiment along with scanning electron microscopy image of CuO nanostructures and water contact angle. (b) Representative image sequences of drop impact dynamics of the water drop with $D_{0} = 2.3 mm$ on a superhydrophobic cylinder having the diameter $D_{c}$ at the impact velocity $U_{0}$ .
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Figure 2
Sequential images of the water drop $(D_{0} = 2.3 mm)$ after impact on a superhydrophobic cylinder, (a) as the cylinder diameter $D_{c}$ varies at the fixed impact velocity $U_{0}$ of 1.02 m/s; and (b) as the impact velocity $U_{0}$ varies at the fixed cylinder diameter of $D_{c} = 9 mm$ . (c) Measured contact time $τ_{c}$ on a superhydrophobic cylinder as a function of the impact velocity $U_{0}$ and cylinder diameter $D_{c}$ for two different drop diameters $D_{0}$ (2.3 and 3.0 mm). (d) Dimensionless contact time as a function of the We number and $D_{c} / D_{0}$ .
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Figure 3
(a) Simulated drop spreading dynamics at $We = 21$ on the cylinder with $D_{c} / D_{0} = 1.5$ . (b) The temporal change of the nondimensional averaged spreading velocity along and transverse to the axial direction when the We number and $D_{c} / D_{0}$ change. (b) The ratio of the maximum spreading velocity along and transverse to the axial direction as a function of $D_{c} / D_{0}$ at the We number of 21 (red circle), and as a function of the We number on the cylinder with $D_{c} / D_{0} = 1.5$ (blue square).
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Figure 4
(a) Schematic of drop impact dynamics on a cylindrical superhydrophobic surface. (b) Retraction regime along the azimuthal direction as a function of the We number and $D_{c} / D_{0}$ for the water drop with $D_{0} = 2.3 mm$ . (c) The maximum spreading ratio $D_{ax, max} / D_{0}$ along the axial direction as a function of the We number and $D_{c} / D_{0}$ for the water drop with $D_{0} = 2.3 mm$ . (d) Normalized retraction velocity along the axial direction as a function of the We number and $D_{c} / D_{0}$ for the water drop with $D_{0} = 2.3 mm$ . Inset shows the temporal change of the spreading diameter along the axial direction at $We \sim 63$ for the different $D_{c} / D_{0}$ .
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Figure 5
Scaling relationship for the contact time on the superhydrophobic cylinder along with the experimental data. (a) Normalized contact time $τ_{c} / τ_{0}$ as a function of $W e^{- 1 / 8} {(D_{c} / D_{0})}^{1 / 4}$ for the experimental data with $D_{c} > D_{0}$ . Inset: drop spreading image with $D_{c} / D_{0} = 6.96$ . (b) Normalized contact time $τ_{c} / τ_{0}$ as a function of $W e^{- 1 / 4} {(D_{c} / D_{0})}^{1 / 2}$ for the experimental data with $D_{c} \leq D_{0}$ . Inset: drop spreading image with $D_{c} / D_{0} = 0.35$ . (c) Normalized contact time $τ_{c} / τ_{0}$ as a function of $W e^{- 1 / 8} {(D_{c} / D_{0})}^{1 / 4}$ for all the experimental data. (d) Comparison of the proposed contact time model with the experimental data from the previous works.
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